Flashcards in Statistics VI - PCA + Meta Exam Questions + Vectors/Matrices Deck (31):

1

## What should the PCA be based on if all variables have the same units?

### the covariance matrix

2

## What should the PCA be based on if variables have different units?

### the correlation matrix

3

## In a PCA of a bivariate distributions: The coordination system is rotated so that ...

### ... the first axis - the first PC - has the largest possible variance.

4

## How come we are allowed to rotate the coordination system in the PCA?

### We are allowed to do that, because the total variance is invariant against rotation of data.

5

##
The sum of squared distances of a distribution = 3.224.

What is the sum of squared distances after rotating the data in the course of a PCA?

### the same: 3.224

6

## The second PC has the ___________ largest variance and is _________ to the first PC.

### The second PC has the SECOND largest variance and is ORTHOGONAL to the first PC.

7

##
What's the total variance in the following (graphically akward) covariance matrix?

[0.950 0.647]

[0.647 0.820]

### 0.950 + 0.820 = 1.770

8

## What multivariate tests should we know?

###
MANCOVA

MANOVA

Hotelling's T²

9

## What univariate tests should we know?

###
student's t-test

ANOVA

ANCOVA

10

## What is an eigenvector and an eigenvalue?

###
If A is a square matrix, v != 0 is an eigenvector of A, if

A * v = λ * v

The number λ is called the eigenvalue of A.

11

## List at least 6 tests!

###
student's t-test

Hotelling's T²

ANOVA

ANCOVA

MANOVA

MANCOVA

12

##
What can the following tests be useful for:

t-test

ANOVA

ANCOVA

###
t-test: difference btw 2 groups and 1 variable

ANOVA: difference btw several groups, one dependent variable

ANCOVA: difference btw several groups, one dependent variable + controls

13

##
What can the following tests be useful for:

Hotelling's T²

MANOVA

MANCOVA

###
Hotelling's T²: difference btw 2 groups and several variables

MANOVA: several dependent variables, groups, interaction among variables

MANCOVA: several dependent variables, groups, interaction among variables + controls

14

## How is the name of a vector usually written in statistics?

### bold lowercase letter

15

## How many columns does a vector have?

### 1

16

## What's the difference between the vector v and the vector v'?

###
v is a column vector and

v' is the transposed version of vector v

17

## In a matrix, what is represented through rows and columns?

###
rows: cases

columns: variables

18

##
How does M' look like if M =

(2 4 1)

(3 8 4)

###
(2 3)

(4 8)

(1 4)

19

## What's the distinct property of a square matrix?

### Same amount of rows and columns.

20

## What's the distinct property of a symmetric matrix?

### S = S'

21

## What's the (main) diagonal of a matrix?

### The "row" of numbers from top left to bottom right.

22

## What is an identity matrix (aka. unit matrix)?

### An identity matrix is a square matrix with ones on the main diagonal.

23

##
Cor(a,b) = 0.8

How large is the explained variance?

### 0.8² = 0.64 -> 64 %

24

##
Cor(a,b) = - 0.3

How large is the explained variance?

### - 0.3² = 0.09 -> 9 %

25

## What's the definition of discrete data?

### Discrete Data can only take certain values.

26

## What's the definition of continuous data?

### Continuous Data is data that can take any value (within a range)

27

## What kind of a scale is Kelvin?

### ratio scale

28

## What kind of a scale is Celsius?

### interval scale

29

## Define precision!

### Degree to which repeated measurements show the same results

30

## Define accuracy!

### Closeness of measurements of a quantity to the quantity's actual (true) value.

31